摘要
将定常结构动力方程的精细积分算法推广应用于非线性动力学问题的求解.对非线性项的线性化处理使该方法的计算精度对时间步长非常敏感,为此将龙贝格积分法引入该方法,提出了由此而产生的指数矩阵的快速精细算法,从而使时间步长的选择具有了自适应性,计算精度和效率均得到提高.
When the precise time - integration algorithm for linear dynamical equations was extended to use in case of nonlinear systems, the processing of linearazation of the nonlinear terms was needed and the calculating precision of the method is very depended on the time step. An effective method is developed to solve the problem by using Romberg integration, and the relative fast algorithm on exponent matrix is given. This efficient method possesses a very good adaptability on choice of time step and very high precision. A numerical example is given to show the calculating precision and efficiency of the method.
出处
《暨南大学学报（自然科学与医学版）》
CAS
CSCD
北大核心
2005年第3期319-323,共5页
Journal of Jinan University(Natural Science & Medicine Edition)
基金
国家自然科学基金(10372036)
广东省自然科学基金(021197)资助项目
关键词
非线性动力学方程
自适应精细积分
龙贝格积分法
nonlinear dynamical equation
adaptive precise integration
Romberg integration
